Final answer:
The potential difference across the mylar sheet inserted between two electrodes connected to a 7.0 V battery remains 7.0 V since the battery maintains the voltage.
Step-by-step explanation:
When we insert a sheet of mylar between two electrodes without disconnecting the battery, the potential difference across the mylar will be the same as the potential difference across the electrodes before the insertion, assuming the mylar does not significantly affect the circuit's voltage. This means that if we had a 7.0 V battery connected to the electrodes, the potential difference across the mylar sheet will also be 7.0 V. This is because the battery continues to maintain a steady potential difference between its terminals, whether the mylar is there or not.